Reference: Abbott, Richard. Analysis and Design of Composite and Metallic Flight Vehicle Structures 3 Edition, 2019
The Allowable stress for bearing compression stress is the material bearing allowable stresses, Fbry at yield or limit level and Fbru at ultimate level.
There is also a failure mode caused by a failure of the material below the surface in a shearing mode.
In general, the peak compression bearing stress can be divided by 3 and compared with the material shear allowable stresses, Fsy at yield or limit level and Fsu at ultimate level.